Statistics Notes for Week 1 ch 4- Pretest

When is a sample statistic biased?

when the average value of the statistic either underestimates or overestimates the corresponding population parameter

When is a sample statistic unbiased?

when the average value of the statistic is equal to the population parameter

Rule: the deviation scores for the an entire set must add up to what?

zero

frequency distribution

this provides an organized summary of the complete set of scores

Steps to calculate variance and standard deviation

1. find # of scores and mean 2. find each deviation 3. square each deviation 4. find sum of all squared deviations (SS) 5. find the MEAN of the squared deviations = this is the VARIANCE 6. find the square root of the variance = this equals the STANDARD DEVIATION

What is the standard deviation for the following set of N=5 scores: 10, 10, 10, 10, and 10?

Because there is no variability (the scores are all the same), the standard deviation is zero

Is it possible to obtain a negative value for the variance or the standard deviation?

The variance and standard deviation are ALWAYS GREATER THAN OR EQUAL TO ZERO. They are measures of distance that are based on squared deviations, which are always positive

Error Variance

explains unexplained and uncontrolled differences b/w scores; as the _____________ increases it becomes more difficult to see any systematic differences of patterns that might exist in the data

What is measured by the population variance?

the _______ is the average squared distance from the mean; (in other words, it equals the MEAN SQUARED DEVIATION

Explain why the formulas for sample variance and population variance are different.

Variance is defined as the mean squared deviation, and, for a population, is computed as the sum of squared deviations divided by N. However, if this same formula is used for a sample, the sample variance will be BIASED and will consistently underestimate the corresponding population value. Therefore, the formula for sample variance includes and adjustment to CORRECT FOR THE BIAS by dividing by df -1 rather than n.

What are the degrees of freedom (the df)?

for a sample of n scores, the _________ for the sample variance are defined as n - 1; determines the number of scores in the sample that are independent and free to vary; the n -1 degrees are the same n -1 used in the formulas for sample variance and standard deviation.

What is measured by the standard deviation?

the _______ provides a measure of the standard, or average, distance from the mean; it is the SQUARE ROOT OF THE VARIANCE

What is range?

the _________ is the distance covered by the scores in a distribution, from the smallest score to the largest score. When the scores are measurements of a continuous variable, the ________ is the difference between the UPPER REAL LIMIT (URL) for the largest score and the LOWER REAL LIMIT (LRL) for the smallest score

What is deviation?

the _________ is the distance from the mean

What is variability?

the __________ provides a quantitative measure of the differences between scores in a distribution and describes the degree to which the scores are spread out or clustered together; high variability tends to obscure any patterns in the data

What is the SS or sum of squares?

the _______is the sum of the squared deviation scores

What happens when you multiply each score by a constant?

this CAUSES the standard deviation to be multiplied by the same constant

What happens when you add a constant to each score does not change the standard deviation. T or F?

this DOES NOT change the standard deviation

measure of variability

this provides a single number that describes the differences that exist from one score to another

measure of central tendency

this summarizes an entire set of scores with a single value that is representative of the whole set

descriptive statistics

to simplify, organize and summarize data so that it is easier for researchers to see patterns